The Cubs and Yankees had one conversation about Dempster, CBSSports.com's Jon Heyman reports. Dempster, according to sources, still strongly prefers to be dealt to the Dodgers, but sources told Heyman that Dempster would agree to go to the Yankees.

The Dodgers and Cubs are about where they have been on the Dempster talks, with the Cubs asking for pitching prospect Allen Webster and the Dodgers saying no.

The Dodgers have begun investigating deals for other pitchers, should they fail to reach a deal with the Cubs on Dempster.

Dempster has spent his whole career in the National League. But Larry Rothschild, his former pitching coach with the Cubs, is now the Yankees pitching coach. Also, former Cubs general manager Jim Hendry now works for the Yankees.

Dempster may also have felt some pressure to say yes, since he already turned down a chance to go to the Braves last week.